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Analysis of a non-reversible Markov chain speedup by a single edge
Published online by Cambridge University Press: 04 January 2023
Abstract
We present a Markov chain example where non-reversibility and an added edge jointly improve mixing time. When a random edge is added to a cycle of n vertices and a Markov chain with a drift is introduced, we get a mixing time of $O(n^{3/2})$ with probability bounded away from 0. If only one of the two modifications were performed, the mixing time would stay $\Omega(n^2)$ .
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- © The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust